EULERIANITY OF FOURIER COEFFICIENTS OF AUTOMORPHIC FORMS
Artikel i vetenskaplig tidskrift, 2021
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.
wave-front set
nilpotent orbit
minimal representation
next-to-minimal representation
Fourier coefficients on reductive groups
Whittaker support
automorphic forms
Euler product
Fourier-Jacobi coefficients
Eisenstein series
automorphic representation
Författare
Dmitry Gourevitch
Weizmann Institute of Science
Henrik Gustafsson
Chalmers, Matematiska vetenskaper, Algebra och geometri
Rutgers University
Institute for Advanced Studies
Axel Kleinschmidt
Max-Planck-Gesellschaft
Université libre de Bruxelles (ULB)
Daniel Persson
Chalmers, Matematiska vetenskaper, Algebra och geometri
Siddhartha Sahi
Rutgers University
Representation Theory
10884165 (eISSN)
Vol. 25 481-507Små automorfa representationer
Vetenskapsrådet (VR) (2018-04760), 2019-01-01 -- 2022-12-31.
Ämneskategorier
Teknisk mekanik
Geometri
Diskret matematik
Matematisk analys
DOI
10.1090/ert/565